Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #13643 |
164 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 117 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(55,62,63,66)(56,68)(57,73)(61,79,67,83)(64,89,86,84)(65,85,87,91)(70,93)(71,94)(74,100)(75,82)(80,105,88,103)(81,104,92,108)(90,112,110,109)(97,113)(101,107)(106,117,111,116);(54,56)(55,61)(57,72)(58,70)(59,71)(60,68)(62,83)(63,67)(64,88)(65,81)(66,79)(69,73)(74,98)(75,99)(76,97)(77,93)(78,94)(80,86)(82,96)(84,103)(85,108)(87,92)(89,105)(90,111)(91,104)(95,100)(101,115)(102,113)(106,110)(107,114)(109,116)(112,117);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55,57,64,58,65,74,90,59,66,75,89,76,91,101,112,60,63,73,86,77,87,100,110,78,62,82,84,102,85,107,109)(56,67,69,88,70,92,95,111,71,83,96,105,97,108,114,117,68,61,72,80,93,81,98,106,94,79,99,103,113,104,115,116)Polycyclic presentation:
2^8,53|a^2=e,c^2=d,e^2=f,f^2=g,g^2=h,b^a=bd,c^a=cg,d^a=dh,i^a=i^52,c^b=ch,e^b=eh,e^c=eh2144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90111);